How to keep texture mapping after applying modifiers
One way to handle this is to use UV Mapping right from the start.  For this, you can press Numpad_7 for top view.   Now if you press Numpad_4 several times, the view will rotate along the z-axis.  Once the positioning matches the texture orientation press Numpad_5 to set the view to Orthographic.  Now press u and select "Project From View (Bounds)"
You could just use Unwrap or Reset but there is no guarantee that you will have the mapping aligned to the texture's direction.  If it's not then you'd have to rotate the UV's and/or scale by -1.0 along one of the axis(that can be confusing, it's best to avoid).



Now you should be able to apply the modifiers and have the following result.